Homework FOUR

• Due Monday, February 17, 2003, at beginning of class.
• Late penalty: 5 points if turned in by 5 p.m., 2/18. 10 points if turned in by noon, Wednesday, 2/19. Not accepted after classtime on 2/19.

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This homework assigment is dedicated to crater counting and is based on images obtained from the Consolidated Lunar Atlas.

The age of a cratered surface can be determined by the number of craters on that surface, under the assumptions that the craters have accumulated steadily over time and no craters have been erased from the surface.

I. In the  full moon image, note the crater at (longitude,latitude) = (3 west, 10 south), almost at the center of this image of the moon.  This is the large crater at the center of image E13.  From the full moon image, estimate the diameter of this crater as a fraction of the lunar diameter (note that you should measure the full diameter of the moon at latitude 0).  This will give you, for your browser, a size scale in km for your measurements of lunar craters.  Estimate the areal size (in km2) of image E13.  We will assume all images are the same size and we will ignore foreshortening effects caused by the spherical surface of the moon.

II. Make a table similar to the following:

 Map\Crater Diameter (km) > 1000 500-1000 200-500 100-200 50-100 10-50 < 10 type of area D10 . . . . . . . mare D19 . . . . . . . mare F12 . . . . . . . highlands E12 . . . . . . . highlands B11 . . . . . . . . G16 . . . . . . . . C11 . . . . . . . . full moon . . . . . . . . Io . . . . . . . . Europa . . . . . . . . Ganymede . . . . . . . . Callisto . . . . . . . .

III.  Use the links in #2, above, to count craters in the at least one of these mare and one highland lunar images.  Use the  full moon image to count the largest craters, taking care not to double count any moderate size craters already counted in one of the close-up images.  Use the links for the Jovian moons to find a 'full moon' image for each of these moons that enables you to make a similar crater count as you did for Earth's moon.

IV. Using the cover image of the Consolidated Lunar Atlas as a guide, you should recognize the dark regions known as the mare (Latin for 'seas') and the brighter regions known as the lunar highlands.  With this distinction in mind, try to answer the following questions:

1. What qualities of craters might you use to determine which craters are old vs. young?
2. Assume the mare are 3.5 BY old (this is when these enormous craters filled with lava and solidified) and that the cratering rate has been steady for the last 3.5 BY.  From your data, what is the cratering rate (craters per 1000 km2) for the production of craters in the smallest 5 size ranges, for the mare regions?
3. Assume the highland regions are 4.5 BY old.   From your data, what is the cratering rate (craters per 1000 km2) for the production of craters in the smallest 5 size ranges, for the highland regions?
4. Since there is no reason why the highlands and the mare should have experienced different cratering rates over the last 3.5 BY, any difference between your answers for the cratering rates of the highlands and the mare must be attributed to events from 3.5-4.5 BY ago.  Do you find the same or different rates?  What do you conclude about the early history of the moon?
5. Tiny objects will burn up in Earth's atmosphere.  But objects large enough to make 1 km diameter (or bigger) craters will drill their way through the atmosphere and create a crater on Earth.  Since Earth and the Moon are in the same part of the solar system, they likely should have experienced similar cratering rates for the last 3.5 BY. Based on this assumption, estimate the number of small (< 10 km diameter; 10-50 km diameter) craters that should have formed on the whole Earth in the last 100,000 years? the last 100 million years? What do you conclude from this?
6. How do the cratering rates for large impacts compare for the four Jovian moons and Earth's moons? What conclusions can you draw about the ages of the surfaces of the Jovian moons?